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Homework Help: Power series

  1. May 2, 2005 #1
    the function [tex]f(x) = \frac{10}{1+100*x^2}[/tex]
    is represented as a power series
    [tex] f(x) = \sum_{n=0}^{\infty} C_nX^n[/tex]

    Find the first few coefficients in the power series:
    C_0 = ____
    C_1 = ____
    C_2 = ____
    C_3 = ____
    C_4 = ____


    well [tex]f(x) = \frac{10}{1+100*x^2}[/tex] can be written as [tex]10\sum_{n=0}^{\infty} (-100x^2)^n[/tex]

    for C_0, i got 10 because if you plug in n = 0, you get 10 (which is correct).
    for c_1, when i plug in n=1, i get -1000, which is incorrect.
    i tried doing the same for c_2-c_4, but it keeps telling me i get the wrong answer. does anyone know why?
     
  2. jcsd
  3. May 2, 2005 #2
    Im pretty sure you modeled the function incorrectly.
     
  4. May 2, 2005 #3

    Galileo

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    Write out a few terms of your expansion. What are the coefficients of the even powers of x in your expansion?
     
  5. May 2, 2005 #4
    and more importantly, what are the coefficients of the odd powers of x?
     
  6. May 3, 2005 #5
    i dont think i modeled it incorrectly, because there's a similar problem in the book, but maybe i made a mistake so who knows, but here are the first few terms....

    10 - 1000x^2 + 10000x^4 -10000000x^6 + 1000000000x^8...

    coefficients of the odd powers are zero....

    but i cant seem to get the even coefficients correctly.... what am i doing wrong?
     
  7. May 3, 2005 #6
    Looks fine to me except that your coefficient for [itex]x^4[/itex] is one power of ten too small. Remember that this expansion is only valid for [itex]|x|<1/10[/itex] too.
     
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